A* Pathfinding

Robotics Engineering

How It Works

The A* pathfinding algorithm is an informed heuristic search strategy that discovers minimum-cost collision-free trajectories between start and target goal coordinates across discrete configuration grids. A* ranks candidate search nodes through the cost function f(n) = g(n) + h(n), where g(n) denotes accumulated cost from the start node and h(n) is an admissible heuristic underestimating remaining distance to the goal. By focusing search effort exclusively along minimal cost contours, A* guarantees global shortest-path optimality with minimal node expansions.

Governing Equation
f(n) = g(n) + h(n) , h(n) = √((x_n - x_{goal})^2 + (y_n - y_{goal})^2)